Various machines have been utilized to cut off short lengths of wire-like or tubular elements at high speed and many of these machines have attempted to cycle the saw at high rate while rotating the saw at a very high rotational speed and cutting single work pieces sequencially in order to attain a high production rate. These machines which cycle the saw at such high rates in a direction laterally of the axis of the saw tend to provide high impact forces of the saw relative to the work in a lateral direction and as a result impose a very high stress and wear factor on the saw, sometimes breaking them while at the same time causing rough cuts of the material which is a particular disadvantage in the manufacture of silver necklace beads, commonly known as liquid silver which are short tubular pieces cut from elongated tubular pieces fed through the machine. Accordingly, many machines of the prior art have been difficult to maintain and have produced cuts which have required substantial tumbling or finishing operations in order to render them smooth enough for the threading thereof into necklaces or the like.